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- Dissection_problem abstract "In geometry, a dissection problem is the problem of partitioning a geometric figure (such as a polytope or ball) into smaller pieces that may be rearranged into a new figure of equal content. In this context, the partitioning is called simply a dissection (of one polytope into another). It is usually required that the dissection use only a finite number of pieces. The Bolyai-Gerwien theorem states that any polygon may be dissected into any other polygon of the same area. It is not true, however, that any polyhedron has a dissection into any other polyhedron of the same volume. This process is possible, however, for any two honeycombs (such as cube) in three dimension and any two zonohedra of equal volume (in any dimension).A dissection into triangles of equal area is called an equidissection. Most polygons cannot be equidissected, and those that can often have restrictions on the possible numbers of triangles. For example, Monsky's theorem states that there is no odd equidissection of a square.".
- Dissection_problem wikiPageExternalLink distile.
- Dissection_problem wikiPageID "2915839".
- Dissection_problem wikiPageRevisionID "587020225".
- Dissection_problem hasPhotoCollection Dissection_problem.
- Dissection_problem subject Category:Discrete_geometry.
- Dissection_problem subject Category:Euclidean_geometry.
- Dissection_problem subject Category:Geometric_dissection.
- Dissection_problem subject Category:Mathematical_problems.
- Dissection_problem subject Category:Polygons.
- Dissection_problem subject Category:Polyhedra.
- Dissection_problem subject Category:Polytopes.
- Dissection_problem type Abstraction100002137.
- Dissection_problem type Attribute100024264.
- Dissection_problem type Condition113920835.
- Dissection_problem type Difficulty114408086.
- Dissection_problem type Figure113862780.
- Dissection_problem type MathematicalProblems.
- Dissection_problem type PlaneFigure113863186.
- Dissection_problem type Polygon113866144.
- Dissection_problem type Polygons.
- Dissection_problem type Problem114410605.
- Dissection_problem type Shape100027807.
- Dissection_problem type State100024720.
- Dissection_problem comment "In geometry, a dissection problem is the problem of partitioning a geometric figure (such as a polytope or ball) into smaller pieces that may be rearranged into a new figure of equal content. In this context, the partitioning is called simply a dissection (of one polytope into another). It is usually required that the dissection use only a finite number of pieces. The Bolyai-Gerwien theorem states that any polygon may be dissected into any other polygon of the same area.".
- Dissection_problem label "Dissection problem".
- Dissection_problem label "Dissezione (matematica)".
- Dissection_problem label "Problème de dissection".
- Dissection_problem label "تشريح شكل".
- Dissection_problem sameAs Problème_de_dissection.
- Dissection_problem sameAs Dissezione_(matematica).
- Dissection_problem sameAs m.08cbff.
- Dissection_problem sameAs Q765035.
- Dissection_problem sameAs Q765035.
- Dissection_problem sameAs Dissection_problem.
- Dissection_problem wasDerivedFrom Dissection_problem?oldid=587020225.
- Dissection_problem isPrimaryTopicOf Dissection_problem.